Unit 3 - Divide & Conquer
3.3 - Split Search
The idea behind divide & conquer is to reduce a larger problem into easier-to-handle smaller "sub-problems" that mimic the larger one.
Imagine you have the entire list of people living in Ottawa-Gatineau in a sorted array as Lastname, Firstname and you wanted to search for a specific person (Smith, Jane) to get their phone number or address or something. The population of the Ottawa-Gatineau area is approximately 1,423,000. You don't know which element in the array is this Smith, Jane you are looking for.
Q. How do we find the index of Smith, Jane efficiently?
A linear approach would be to start at index 0 and check each element if it is equal to the target value. This would be a very inefficient method with the worst-case having to look-at and compare all elements in the array.
Modified Linear Search
A slightly more efficient method would be to check the first letter of the target (in this case, "S"). Since "S" is closer to "Z" than "A", we could perform the linear search in reverse and potentially find the target faster.
Let's play a guessing game. I'm thinking of a number between 1 and 1,000,000. I will tell you if your guesses are too high or low. What is the smartest number to select to start? How about for your second guess?
A much more efficient search method is to exploit the fact that the list is sorted. Start in the middle (or the left of middle if there's an even #) and split left/right - repeat! Split Search is more efficient (faster) than linear because it starts at the middle of a sorted array (or list) and eliminates half of the array each pass through the algorithm. Note - this only works on sorted data.
Notice that the algorithm needs to take into account an even or odd number of elements in each iteration. The programmer will need to decide which "side" gets the extra element in an odd number - typically the right half, but there is no specific rule.
Also, the element may not exist. In this case we either return -1, undefined, null, or similar.